I've heard people say they've measured BP with the plastic powder measure but they have to clean it after every use. Why?

The reason for cleaning the Hornady, Lyman and RCBS powder measures after each use is not the plastic hopper. It's the hygroscopic or corrosive nature of BP and substitutes that freezes the rotors. APP being the worst - it'l lock up a rotor while in use -, and real BP being the most forgivng.

I've never used a Lee powder measure so cannot speak to the necessity of cleaning them after use.